* Vote on new constitution in less than two weeks (Updates death toll, soldiers injured in Sinai)

By Maggie Fick

CAIRO, Jan 3 (Reuters) - Eleven people were shot dead as supporters of the Muslim Brotherhood clashed with police across Egypt on Friday, defying an ever-widening state crackdown on the movement that ruled the country until six months ago.

Islamists opposed to the army's overthrow of President Mohamed Mursi in July have been holding daily demonstrations, even after the army-backed government declared his Brotherhood a terrorist group last week, increasing the penalties for dissent.

The government is using the new classification to detain hundreds of Brotherhood supporters. Thousands more, including top leaders of the group, have been in jail for months, arrested in the aftermath of the army takeover.

The crackdown has reduced but not entirely broken the ability of the Brotherhood to mobilise protests. It has lately been relying on students to sustain momentum against what it refers to as the "putschist regime" governing Egypt.

In the Cairo district of Nasr City riot police in bulletproof vests fired teargas at protesters throwing fireworks and stones. Similar clashes erupted across the country, as has become commonplace after midday prayers each Friday, not a working day in Egypt.

The Health Ministry said three protesters were killed in different districts in Cairo. A security source said they died from bullet wounds, though it was unclear if the police or armed civilians had shot them.

In a separate incident, showing the deepening divisions since Mursi was ousted, a man yelling insults at pro-Brotherhood demonstrators marching near his house was shot dead by the protesters, a security source said.

A male protester and a woman were shot dead in the coastal city of Alexandria, medical and security sources said. It was not clear whether the woman was a protester or an onlooker.

Another demonstrator was shot dead by police in the Suez Canal city of Ismailia after a march set off from a mosque after midday prayers, medical sources said.

In the rural province of Fayoum, southwest of Cairo, three protesters, including a student, died from bullet wounds to the chest and head, local Health Ministry official Medhat Shukri told Reuters.

Another university student was shot dead during clashes in the southern town of Minya. The Health Ministry said 42 people were wounded nationwide.

Police arrested 122 Brotherhood members for possession of weapons, the Interior Ministry said in a statement. The Brotherhood says its supporters are unarmed.

CONSTITUTION VOTE

The power of the Brotherhood - the country's oldest and best organised Islamist movement - has been dramatically eroded by the arrests, having its leaders' assets frozen and the designation of the group as a terrorist organisation.

A new constitution to be voted on at a referendum on Jan. 14-15 will also ban religiously based political parties and give more power to the military.

The army-backed authorities says the constitution will pave the way for a return to democratic rule by mid-year.

It would be a further step toward the complete removal of the Brotherhood from public life after winning every election in Egypt since autocrat Hosni Mubarak was overthrown in the 2011.

Authorities have pledged to secure the referendum, despite the daily protests and frequent bomb attacks against the security services over the past months.

They blame the Brotherhood for the unrest. The Brotherhood says it is committed to peaceful activism.

A conservative estimate puts the overall death toll since Mursi's fall at well over 1,500. Most of those killed have been Mursi supporters, including hundreds gunned down when the security forces cleared a protest vigil outside a Cairo mosque.

About 350 police and soldiers have been killed in bombings and shootings since Mursi was ousted.

Four soldiers were injured by an explosion caused by a roadside bomb apparently targeting a military convoy in the volatile North Sinai area, security sources said.

Although the majority of the attacks on security forces have occurred in the Sinai Peninsula, which borders Israel and the Gaza Strip, bomb attacks in recent weeks in the Nile Delta suggest a widening reach of militant attacks that have become commonplace since the army toppled Mursi. (Reporting by Yusri Mohamed in Ismailia and Mohamed Abdalla, Omar Fahmy, Yasmine Saleh, and Reuters TV in Cairo; Writing by Maggie Fick; Editing by Alison Williams)